Distributed Database Management Systems: Lecture 14

Distributed Database
Management Systems

Lecture 14


Minterm predicates:
given a set of simple predicates
Pr = {pr1, pr2, …, pm}for a relation R, the
set of minterm predicates M is defined
as

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M = {m1, m2, ……, mz}
M = {mj | mj = p*k}, 1 ≤ k ≤ m, 1 ≤ j
≤z
p ∈ Pr
k

where p*k = pk or p*k = (pk)

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PAY(title, sal)

p1: title = “El Eng”
p2: title = “Sys Ana”
p3: title = “Mech Eng”
p4: title = “Prog”
p5: SAL ≤ 20,000
p6: SAL > 20000
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Minterm Predicates

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m1: title = “El Eng”
m2: title = “Sys Ana”

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SAL ≤ 20,000
SAL > 20,000

6


PHF-Requirements

3- minterm selectivities sel(mi):
number of tuples of the relation that
would be accessed by a user query
involving mi. Like, sel(m1) = 0 as
per data on p108

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4- Access frequencies acc(qi):
frequency with which user
applications access data. If Q(q1,
q2, …, qn} is set of user queries,
then acc(qi) determines the
access frequency of qi within a
given period, like acc(q2) = 24
5- Access frequencies minterm
acc(mi) can also be defined from
acc(q
)
i
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• A PHF is defined by a selection
operation on the owner
relations of the database

schema, given a relation R, its
PHF are given by
Ri = Fi
(R), 1 ≤ i ≤ w
– Where Fj is a selection formula,
which is (preferably) a minterm
predicate.
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PHF (Simple Example)

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PAY
Title

Sal

Elect. Eng

40000

Sys Analyst

34000

Mech. Eng

27000

Programmer

24000

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PAY1 = σ sal ≤ 30000  (PAY)
PAY2 = σ sal > 30000 (PAY)
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Title

Sal

Elect. Eng

40000

Sys Analyst

34000

PAY1

PAY2

Title

Sal

Mech. Eng

27000

Programmer

24000

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• Defining simple predicates may be
tricky
– in case of continuous domain
– Balance in Fragments’ Size

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A set of simple predicates Pr is said to
be complete if the accesses to the
tuples of the minterm fragments
defined on Pr requires
that two tuples of the same minterm
fragment have the same probability of
being accessed by the application.

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Completeness Example

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PROJ
pNo

pName

budget

Loc

P1

Instrumentation

3.5M

Lahore

P2

Database Dev.

2.3M

Rawalpindi

P3

CAD/CAM

1.9M

Rawalpindi

P4

Maintenance

1.6M

Peshawar

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–Find the budgets of projects at
each location. (1)
–Find projects with budgets less
than 2M. (2)

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• According to (1),
Pr = {LOC=“Lahore”,
LOC=“Rawalpindi”,
LOC=“Peshawar”}

• Which is not complete with respect to
(2).

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Modify
Pr = {LOC=“Lahore”,
LOC=“Rawalpindi”, LOC=“Peshawar”,
BUDGET<=200000, BUDGET
>200000}
• Which is complete.

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Thanks